Büchi automata for distributed temporal logic

Computing Research Repository, 2003

We introduce a temporal logic to reason on global applications in an asynchronous setting. First, we define the Distributed States Logic (DSL), a modal logic for localities that embeds the local theories of each component into a theory of the distributed states of the system. We provide the logic with a sound and complete axiomatization. The contribution is that it is possible to reason about properties that involve several components, even in the absence of a global clock. Then, we define the Distributed States Temporal Logic (DSTL) by introducing temporal operatorsà la Unity. We support our proposal by working out a pair of examples: a simple secure communication system, and an algorithm for distributed leader election. The motivation for this work is that the existing logics for distributed systems do not have the right expressive power to reason on the systems behaviour, when the communication is based on asynchronous message passing. On the other side, asynchronous communication is the most used abstraction when modelling global applications.

ACM Transactions on Programming Languages and Systems, 1989

An approach to proving temporal properties of concurrent programs that does not use temporal logic as an inference system is presented. The approach is based on using Buchi automata to specify properties. To show that a program satisfies a given property, proof obligations are derived from the Buchi automata specifying that property. These obligations are discharged by devising suitable invariant assertions and variant functions for the program. The approach is shown to be sound and relatively complete. A mutual exclusion protocol illustrates its application.

Frontiers of Combining Systems, 2005

In this paper, we introduce a spatial and temporal logic for reasoning about distributed computation. The logic is a combination of an extension of hybrid logic, that allows us to reason about the spatial structure of a computation, and linear temporal logic, which accounts for the temporal aspects. On the pragmatic side, we show the wide applicability of this logic by means of many examples. Our main technical contribution is completeness of the logic both with respect to spatial/temporal structures and a class of spatial transition systems.

1999

We present a model checking algorithm for LCSA, a temporal logic for communicating sequential agents (CSAs) introduced by Lodaya, Ramanujam, and Thiagarajan. LCSA contains temporal modalities indexed with a local point of view of one agent and allows to refer to properties of other agents according to the latest gossip which is related to local knowledge. The model checking procedure relies on a modularisation of LCSA into temporal and gossip modalities. We i n troduce a hierarchy of formulae and a corresponding hierarchy of equivalences, which allows to compute for each formula and nite state distributed system a nite multi modal Kripke structure, on which the formula can be checked with standard techniques. ? This work was partially supported by the DFG within SFB 342 (A3), and within the priority program \Design and design methodology of embedded systems", and by the EEC program on Training and Mobility in Research (TMR). The work was done while the second author was a liated with the Univ. of Hildesheim, Germany.

Journal of Logic, Language and Information, 2010

We suggest that developing automata theoretic foundations is relevant for knowledge theory, so that we study not only what is known by agents, but also the mechanisms by which such knowledge is arrived at. We define a class of epistemic automata, in which agents' local states are annotated with abstract knowledge assertions about others. These are finite state agents who communicate synchronously with each other and information exchange is 'perfect'. We show that the class of recognizable languages has good closure properties, leading to a Kleene-type theorem using what we call regular knowledge expressions. These automata model distributed causal knowledge in the following way: each agent in the system has a partial knowledge of the temporal evolution of the system, and every time agents synchronize, they update each other's knowledge, resulting in a more up-to-date view of the system state. Hence we show that these automata can be used to solve the satisfiability problem for a natural epistemic temporal logic for local properties. Finally, we characterize the class of languages recognized by epistemic automata as the regular consistent languages studied in concurrency theory.

2001

In this paper, we define a new class of combined automata, called temporalized automata, which can be viewed as the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Furthermore, we successfully apply temporalized automata to provide the full secondorder theory of k-refinable downward unbounded layered structures with a temporal logic counterpart. Finally, we show how temporalized automata can be used to deal with relevant classes of reactive systems, such as granular reactive systems and mobile reactive systems.

Logics in Artificial Intelligence, 2004

In this paper we address the problem of specifying and verifying systems of communicating agents in a Dynamic Linear Time Temporal Logic (DLTL). This logic provides a simple formalization of the communicative actions in terms of their effects and preconditions. Furthermore it allows to specify interaction protocols by means of temporal constraints representing permissions and commitments. Agent programs, when known, can be formulated in DLTL as complex actions (regular programs). The paper addresses several kinds of verification problems including the problem of compliance of agents to the protocol, and describes how they can be solved by model checking in DLTL using automata.

2011

In distributed real-time systems, we cannot assume that clocks are perfectly synchronized. To model them, we use independent clocks and define their timed semantics. The universal timed language, and the timed language inclusion of icTA are undecidable. Thus, we propose Recursive Distributed Event Clock Automata (DECA). DECA are closed under all boolean operations and their timed language inclusion problem is decidable (more precisely PSPACE-complete), allowing stepwise refinement.

1997

We describe an automata-theoretic approach to the automated checking of truth and validity for temporal logics. The basic idea underlying this approach is that for any formula we can construct an alternating automaton that accepts precisely the models of the formula. For linear temporal logics the automaton runs on infinite words while for branching temporal logics the automaton runs on infinite trees.

2005

This article deals with a distributed, fault-tolerant real-time application modeling by timed automata. The application under consideration consists of several processors communicating via Controller Area Network (CAN); each processor executes an application that consists of fault-tolerant tasks running under an operating system (e.g. OSEK) and using inter-task synchronization primitives. For such system, the model checking tool (e.g. UPAALL) can be used to verify complex time and logical properties formalized as a safety or bounded liveness properties (e.g. end-to-end response time considering occurrence of a fault, state reachability). The main contribution of this paper is that the proposed model reduces size of the statespace by sharing clocks measuring the execution time of tasks and simply incorporates fault-tolerant features of the application.